Mathematics: Can someone please explain how to do this problem? The websites instructions are very poor. Rewrite and as equivalent rational expressions with the lowest common denominator.

Can someone please explain how to do this problem?

Ответ:

dcox5057

29.01.2022

Mathematics

x = -5

Step-by-step explanation:

If you factor each denominator, you can find the LCM.

$\dfrac{2}{x^2-x-12}=\dfrac{1}{x^2-16}\\\\\\\dfrac{2}{(x-4)(x+3)}=\dfrac{1}{(x-4)(x+4)}\\\\\\\text{The LCM is (x-4)(x+4)(x+3)}\\\\\\\dfrac{2}{(x-4)(x+3)}\bigg(\dfrac{x+4}{x+4}\bigg)=\dfrac{1}{(x-4)(x+4)}\bigg(\dfrac{x+3}{x+3}\bigg)\\\\\\\dfrac{2(x+4)}{(x-4)(x+4)(x+3)}=\dfrac{1(x+3)}{(x-4)(x+4)(x+3)}\\$

Now that the denominators are equal, we can clear the denominator and set the numerators equal to each other.

2(x + 4) = 1(x + 3)

2x + 8 = x + 3

x + 8 = 3

x = -5

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Ответ:

skent1423

28.03.2021

Mathematics

Q 5.9

Step-by-step explanation:

Que el dinero gastado por Juan sea x

Deja que el dinero gastado por Carolina sea y

Si el dinero total gastado es Q 15

Luego;

x + y = 15 (1)

De la segunda oración;

y = x + 3,2 (2)

Sustituyendo (2) en (1)

x + x + 3,2 = 15

2x + 3,2 = 15

2x = 15 - 3,2

2x = 11,8

x = 5,9

x = Q 5.9

Por lo tanto Juan gastó Q 5.9

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Can someone please explain how to do this problem? The websites instructions are very poor. Rewrite $\frac{2}{x^{2} -x-12}$ and $\frac{1}{x^{2}-16 }$ as equivalent rational expressions with the lowest common denominator.

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